Question: Simplify the following expression: $p = \dfrac{k^2 + 2k - 3}{k - 1} $
Solution: First factor the polynomial in the numerator. $ k^2 + 2k - 3 = (k - 1)(k + 3) $ So we can rewrite the expression as: $p = \dfrac{(k - 1)(k + 3)}{k - 1} $ We can divide the numerator and denominator by $(k - 1)$ on condition that $k \neq 1$ Therefore $p = k + 3; k \neq 1$